A Practical Technique for Spectral Analysis of Nonlinear Systems Under Stochastic Parametric and External Excitations

[+] Author and Article Information
R. J. Chang

Department of Mechanical Engineering, National Cheng Kung University, Tainan, Taiwan 70101 Republic of China

J. Vib. Acoust 113(4), 516-522 (Oct 01, 1991) (7 pages) doi:10.1115/1.2930216 History: Received July 01, 1990; Revised January 01, 1991; Online June 17, 2008


A practical approach is developed for analyzing the spectral response of a nonlinear system subjected to both parametric and external Gaussian white noise excitations. The technique is implemented through the combined methods of equivalent external excitation and equivalent linearization to derive an equivalent linear system under equivalent external noise excitation. The spectral response is then obtained through utilizing the input/output spectral relation and covariance matching condition. A parametric noise excited linear system, Duffing oscillator, and nonlinear system with hysteretic nonlinearity are selected for investigation. The validity of the proposed method for analyzing spectral response is further supported by some analytical solutions and FFT technique through Monte Carlo simulations.

Copyright © 1991 by The American Society of Mechanical Engineers
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